Method and apparatus for phase reference tracking of digital phase modulated signals in the receiver

ABSTRACT

The present invention discloses a method and apparatus to provide, effectively and robustly, a phase reference in phase-domain for digital phase-modulated signals. Not only the first-order but also higher order PLLs are delineated for robust and fast tracking of frequency errors and time-varying frequency errors between the transmitter and the receiver. This invention can be applied to any phase-modulated signal such as PSK, DPSK, π/4-DPSK, and CPM. The decoders with this invention can achieve close to the performance of coherent detection. 
     Reference
     [1] D. Divsalar and M. K. Simon, “Multiple-symbols differential detection of MPSK,”  IEEE Trans. Commun.,  vol. 38, pp. 300-308, March 1990.   [2] Specification of the Bluetooth System, 2.0+EDR, 4 Nov. 2004

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to digital communicationsystems, and more particularly to a methods and apparatus for phasereference tracking of digital phase modulated signals in the receiver.

2. Background

Digital phase modulation is one of the popular digital modulations dueto its simplicity and robustness. Source information is transmitted byselecting phases of the signal according to the information bits.Continuous phase modulation (CPM), Phase-shift keying (PSK) anddifferential phase-shift keying (DPSK) are examples of digital phasemodulation.

In the receiver, it is necessary to detect an accurate phase referencefor decoding the transmitted information bits. Otherwise, phasereference errors may cause significant performance degradation. Fordifferentially encoded digital phase modulations such as DPSK, DQPSK andD8PSK, a phase reference can be derived from the previous symbol tofacilitate the demodulation. For simple receivers, DPSK signals may bedifferentially decoded. That means, previous phase is used as areference for the current symbol. However, since this reference isnoisy, the performance can degrade up to 3 dB, compared to theperformance with perfect phase reference. Phase reference tracking isalso useful for DPSK signals.

To facilitate such a phase reference estimate, a training sequence isoften transmitted at the beginning of a data packet. The phase referencemay be easily estimated with the training sequence known at thereceiver, but the throughput may be slightly decreased as the trainingsequence does not contain source information. Moreover, the phasereference may be time-varying due to the imperfect oscillators at thetransmitter (TX) or the receiver (RX). In this case, phase referencetracking will be necessary for the receiver to maintain best performancewhile receiving information bits. Phase references may be heavilytime-varying due to the mismatching between TX and RX oscillators. Thismismatching is so-called frequency offset (FO). Moreover frequency driftmay cause difficulty in tracking accurate phase reference. By estimatingand/or tracking this FO, phase reference may be kept accurate.

For this phase reference tracking, multiple symbol detection [1] basedon maximum likelihood sequence detection (MLSD) was proposed, but itscomplexity exponentially increases with the number of observationsymbols. Furthermore, U.S. Pat. No. 7,245,672 issued to Smit et al.,entitled “Method and apparatus for phase-domain semi-coherentdemodulation” disclosed that a first-order IIR filter in phase-domain,of which complexity further decreases due to the phase operationsinstead of the complex signal operations as shown in FIG. 3, However,this first order phase tracking is not sufficient to handle heavy phasevariations. For example, Bluetooth spec [2] allows frequency to drift upto 400 Hz/μs. Also, double errors (decoded symbol error propagation) areun-avoidable in this invention due to the proposed differentialdecoding.

According to above problems, the related field needs a simple and robustphase tracking method, where the phase reference is tracked inphase-domain with a high order digital phase-locked loop, for generalphase-modulated signals. Also, related field suggests a better way totrack phase for differentially encoded digital phase modulations, suchas DBPSK, (π/4) DQPSK and DBPSK modulated signals.

BRIEF SUMMARY OF THE INVENTION

It is an objective of the present invention to provide an effective androbust method for phase reference tracking of digital phase modulatedsignals in the receiver. It tracks the phase errors and generatesreliable phase reference to estimate.

To achieve the above objective, the present invention provides a methodused for phase reference tracking of digital phase modulated signals inthe receiver, comprising the steps of: converting a received complexsignal to the received phase r_(n), feeding the received phase r_(n) toa phase reference tracking unit, producing an estimated transmit phase{tilde over (s)}_(n) from the phase reference tracking unit, feeding theestimated transmit phase {tilde over (s)}_(n) to a coherent decoder, andproducing a decoded symbol â_(n) from the coherent decoder.

According to one aspect of the present invention, the received complexsignal can be encoded by BPSK, MPSK, PSK and DPSK modulation systems.

According to one aspect of the present invention, the received phaser_(n) can be converted to different forms according the received complexsignal.

Another objective of the present invention is to provide an effectiveand robust apparatus for phase reference tracking of digital phasemodulated signals in the receiver. The phase reference tracking unittakes the received phase and the decoded symbols as its input, generatesreliable phase reference to estimate by tracking phase errors due tofrequency offset and the variation of frequency offset. A gradientalgorithm in phase-domain based on the measured phase error is utilizedin the phase reference tracking unit.

To achieve the above objective, the present invention provides anapparatus used for phase reference tracking of digital phase modulatedsignals in the receiver, comprising: a complex-to-phase converter, usedfor converting the in-phase (I_(n)) and the quadrature (Q_(n))components of a received complex signal to a received phase r_(n), thephase reference tracking unit, which is electrically connected to thecomplex-to-phase converter, used for producing an estimated transmitphase {tilde over (s)}_(n), and the coherent decoder, which iselectrically connected to the phase reference tracking unit, used forproducing a decoded symbol â_(n) and sending a re-modulation phasesignal ŝ_(n) to the phase reference tracking unit.

According to one aspect of the present invention, the apparatus used forphase reference tracking of digital phase modulated signals in thereceiver can be applied in BPSK, MPSK, PSK and DPSK modulation systems.

According to one aspect of the present invention, the types of thecoherent decoder can be selected according to BPSK, MPSK and DPSKmodulation systems.

BRIEF DESCRIPTION OF THE DRAWINGS

All the objects, advantages, and novel features of the invention willbecome more apparent from the following detailed descriptions when takenin conjunction with the accompanying drawings.

FIG. 1 is a block diagram for a general decoder and the invented phasereference tracking;

FIG. 2 is a block diagram for the PSK decoder and the invented phasereference tracking;

FIG. 3 is a DPSK receiver block diagram proposed by Smit (Prior Art);

FIG. 4 is a block diagram for a DPSK decoder and the invented phasereference tracking; and

FIG. 5 is an alternative block diagram for a DPSK decoder and theinvented phase reference tracking.

DETAILED DESCRIPTION OF THE INVENTION

Although the invention has been explained in relation to severalpreferred embodiments, the accompanying drawings and the followingdetailed descriptions are the preferred embodiment of the presentinvention. It is to be understood that the following discloseddescriptions will be examples of present invention, and will not limitthe present invention into the drawings and the special embodiment.

Phase reference tracking is not necessary for some phase-modulatedsignals such as Gaussian frequency shift-keying (GFSK) and DPSK.However, it is well-known that coherent detection may help to improveperformances up to 3 dB. Here, a simple, robust and generalized methodfor phase reference tracking in phase-domain is provided.

To understand the spirit of the present invention, referring to FIG. 1,it shows the block diagram for a general decoder and the invented phasereference tracking. An apparatus for phase reference tracking of digitalphase modulated signals in the receiver 100 comprises a complex-to-phaseconverter 110, a phase reference tracking unit 120, a coherent decoder130. The complex-to-phase converter 110 is used for converting thein-phase (I_(n)) and the quadrature (Q_(n)) components of a receivedcomplex signal 101 to a received phase r_(n) 111. The phase referencetracking unit 120, which is electrically connected to thecomplex-to-phase converter 110, is used for producing an estimatedtransmit phase {tilde over (s)}_(n) 141. The coherent decoder 130, whichis electrically connected to the phase reference tracking unit 120, isused for producing a decoded symbol â_(n) 212 and sending are-modulation phase signal ŝ_(n) 149 to the phase reference trackingunit 120.

The apparatus used for phase reference tracking of digital phasemodulated signals in the receiver can be applied in BPSK, MPSK, PSK andDPSK modulation systems. The received complex signal 101 can be encodedby BPSK, MPSK, PSK and DPSK modulation systems. The received phase r_(n)111 can be converted to different forms according to the receivedcomplex signal 101. The types of the coherent decoder 130 can beselected according to BPSK, MPSK and DPSK modulation systems.

Now, referring to FIG. 1, the phase reference tracking unit furthercomprises a first subtracter 121, a second subtracter 122, a firstmultiplier 123, a first adder 124, a first sample delay unit 125, asecond multiplier 126, a second adder 127, a third adder 128, and asecond sample delay unit 129. The first subtracter 121 is used forsubtracting the previous phase reference estimate {tilde over (θ)}_(n-1)142 from the received phase r_(n) 111 and producing the estimatedtransmit phase {tilde over (s)}_(n) 141. The second subtracter 122,which is electrically connected to the coherent decoder 130, is used forsubtracting the re-modulation phase signal ŝ_(n-d) 131 from theestimated transmit phase {tilde over (s)}_(n) 141 and producing atracking error ε_(n) 145. The first multiplier 146, which iselectrically connected to the second subtracter 122, is used for scalingthe tracking error ε_(n) 145 by a value of β 146. The first adder 124,which is electrically connected to the first multiplier 123, is used foradding a scaled tracking error βε_(n) and a previous phase correctionfactor {tilde over (θ)}′_(n-1). The first sample delay unit 125, whichis electrically connected to the first adder 124, is used for taking thephase correction factor {tilde over (θ)}′_(n) 147 to the previous stateof {tilde over (θ)}′_(n-1) and providing a feedback signal of previousphase correction factor {tilde over (θ)}′_(n-1) to the first adder 124.The second multiplier 126, which is electrically connected to the secondsubtracter 122, is used for scaling the tracking error ε_(n) 145 by avalue of a 143. The second adder 127, which is electrically connected tothe second multiplier 126, is used for adding a scaled tracking errorαε_(n) and the phase correction factor {tilde over (θ)}′_(n) 147. Thethird adder 128, which is electrically connected to the second adder127, is used for adding the previous phase reference estimate {tildeover (θ)}_(n-1), the scaled tracking error αε_(n) and the phasecorrection factor {tilde over (θ)}′_(n) 147. The second sample delayunit 129, which is electrically connected to the second adder, is usedfor the taking the phase reference estimate {tilde over (θ)}_(n) 147 tothe previous state {tilde over (θ)}_(n-1) and providing a feedbacksignal of previous reference estimate {tilde over (θ)}_(n-1) to thethird adder 128 and the first subtracter 121.

Moreover, to compensate the delay (d) caused in the coherent decoder andto generate the estimated transmit phase {tilde over (s)}_(n) 149 withcorrect timing, a coherent decoder 140, which is electrically connectedto the first subtracter 121, is provided. Therefore, the estimatedtransmit phase {tilde over (s)}_(n) 149 and the decoded symbol â_(n) 212turn into a estimated transmit phase with a delay (d) {tilde over(s)}_(n-d) 144 and decoded symbol with a delay (d) â_(n-d) 132 which arealso denoted as decoded symbols 133.

The construction of the block diagram of the apparatus according thepresent invention may be modified and/or simplified with combining thephase reference tracking units and the coherent decoder units byremoving redundant units and/or re-organizing the block diagrams.

Besides, the procedure of the present invention can further described asthe following steps:

-   -   Step1: converting a received complex signal to the received        phase r_(n) 111;    -   Step2: feeding the received phase r_(n) 111 to a phase reference        tracking unit;    -   Step3: producing an estimated transmit phase ŝ_(n) 141 from the        phase reference tracking unit;    -   Step4: feeding the estimated transmit phase {tilde over (s)}_(n)        141 to a coherent decoder; and    -   Step5: producing a decoded symbol â_(n) 212 from the coherent        decoder.

The received complex signal can be encoded by BPSK, MPSK, PSK and DPSKmodulation systems. The received phase r_(n) 111 can be converted todifferent forms according to the received complex signal.

Moreover, the procedure of producing an estimated transmit phase {tildeover (s)}_(n) 141 further comprising the steps of:

-   -   Step1: subtracting a previous phase reference estimate {tilde        over (θ)}_(n-1) 142 from a received phase r_(n) 111;    -   Step2: producing a tracking error ε_(n) 145 by subtracting a        re-modulation phase signal ŝ_(n) 149 from an estimated transmit        phase {tilde over (s)}_(n) 141;    -   Step3: scaling the tracking error ε_(n) 145 by a value of β 146;    -   Step4: adding the scaled of tracking error βε_(n) with a        previous phase correction factor {tilde over (θ)}′_(n-1) and        derive a phase correction factor {tilde over (θ)}′_(n);    -   Step5: scaling the tracking error ε_(n) 145 by a value of α 143;    -   Step6: adding the scaled of tracking error αε_(n) with the phase        correction factor {tilde over (θ)}′_(n); and    -   Step7: adding the scaled of tracking error αε_(n) with the phase        correction factor {tilde over (θ)}′_(n) with the previous phase        reference estimate {tilde over (θ)}_(n-1) and derive the phase        reference estimate {tilde over (θ)}_(n) 148.

The procedure of producing an estimated transmit phase {tilde over(s)}_(n) further comprising the steps of:

-   -   Step1: subtracting a previous phase reference estimate {tilde        over (θ)}_(n-1) from a received phase r_(n) 111;    -   Step2: adding a delay (d) to an estimated transmit phase {tilde        over (s)}_(n) 141;    -   Step3: producing a tracking error ε_(n) 145 by subtracting a        re-modulation phase with a delay (d){tilde over (s)}_(n-d) 131        from a re-modulation phase with a delay (d){tilde over        (s)}_(n-d) 131;    -   Step4: scaling the tracking error ε_(n) by a value of β;    -   Step5: adding the scaled of tracking error βε_(n) with a        previous phase correction factor {tilde over (θ)}′_(n-1) and        derive a phase correction factor {tilde over (θ)}′_(n);    -   Step6: scaling the tracking error ε_(n) 145 by a value of α 143;    -   Step7: adding the scaled of tracking error αε_(n) with the phase        correction factor {tilde over (θ)}′_(n); and    -   Step8: adding the scaled of tracking error αε_(n) with the phase        correction factor {tilde over (θ)}′_(n) with the previous phase        reference estimate {tilde over (θ)}_(n-1) and derive the phase        reference estimate {tilde over (θ)}_(n) 148.

The delay (d) is used for generating the estimated transmit phase {tildeover (s)}_(n) 141 with correct timing.

The procedure of producing a decoded symbol â_(n) 212 further comprisingthe steps of:

-   -   Step1: feeding an estimated transmit phase {tilde over (s)}_(n)        141 to a coherent decoder;    -   Step2: de-mapping the estimated transmit phase {tilde over        (s)}_(n) 141;    -   Step3: producing a decoded symbol â_(n) 212;    -   Step4: mapping the decoded symbol â_(n) 212; and    -   Step5: producing a re-modulation phase signal ŝ_(n) 141;

The re-modulation phase signal ŝ_(n) 141 is feed to a phase referencetracking unit and used for the calculation of a tracking error ε_(n)145. The method used for phase reference tracking of digital phasemodulated signals in the receiver as described above, the method isgeneralized with n-th order tracking.

A complex-to-phase converter 110 converts the incoming received complexsignal 101, consisting of the in-phase (I_(n)) and the quadrature(Q_(n)) components, to a received phase r_(n) 111 using the followingequation:

$\begin{matrix}{{r_{n} = {\tan^{- 1}\left( \frac{Q_{n}}{I_{n}} \right)}},} & {{Eq}.\mspace{14mu} (1)}\end{matrix}$

where n represents the symbol time index. Note that the operations onphase are based on modular 2π. The received phase r_(n) 111 can beconverted to different forms according the received complex signal andalso can be converted to different forms according the received complexsignal 101.

This received phase r_(n) 111 is fed to a phase reference tracking unit120, which produces an estimated transmit phase {tilde over (s)}_(n)141. This estimated transmit phase {tilde over (s)}_(n) 141 is anestimated transmit phase and is fed to a coherent decoder 130. Since theallowed transmit phase is quantized for a digital phase modulation, thecoherent decoder 130 decodes the estimated transmit phase {tilde over(s)}_(n) 141 based on a de-mapping table to produce the decoded symbolwith a delay (d) â_(n-d) 132. For example, the coherent decoder 130decodes for BPSK can be found in TABLE 1 below. If required, thecoherent decoder 130 may utilize the received complex signal 101. Thecoherent decoder 130 also uses a “mapping” table to reconstruct thephase (also known as re-modulation) for the decoded symbol â_(n) 132,denoted ŝ_(n-d) 131, and sends it to the phase reference tracking unit120. An example for the mapping table for BPSK modulated signal is shownin Table 2 below.

TABLE 1 De-Mapping Table for BPSK {tilde over (s)}_(n) Decoded Symbol−π/2 < {tilde over (s)}_(n) < π/2 0 Otherwise 1

TABLE 2 Mapping Table for BPSK Decoded Symbol Re-modulated Phase 0 0 1 π

Inside the phase reference tracking unit 120, the estimated transmitphase {tilde over (s)}_(n) 141 at the receiver is calculated bysubtracting the previous phase reference estimate {tilde over (θ)}_(n-1)142 from r_(n) 111. A tracking error ε_(n) 145 is calculated bysubtracting ŝ_(n-d) 131 from {tilde over (s)}_(n-d) 144, where d is adelay introduced by the coherent decoder 130. Then, a phase correctionfactor due to frequency error, {tilde over (θ)}′_(n) 147, and a phasereference estimate, {tilde over (θ)}_(n) 148, are updated with thewell-known gradient method:

{tilde over (θ)}′_(n)={tilde over (θ)}′_(n-1)+βε_(n),   Eq. (2a)

{tilde over (θ)}_(n)={tilde over (θ)}_(n-1)+αε_(n)+{tilde over(θ)}′_(n),   Eq. (2b)

where 0≦α≦1 and 0≦β≦1. Note that {tilde over (θ)}′_(n) 147 is aphase-error correction factor based on an estimated frequency-offsetbetween the TX and the RX. Such a phase tracking loop is traditionallyknown as a second order phase-locked-loop (PLL). This tracking schemecan be easily generalized to a third order PLL as follows:

{tilde over (θ)}″_(n)={tilde over (θ)}″_(n-1)+γε_(n), Eq. (3a)

{tilde over (θ)}′_(n)={tilde over (θ)}′_(n-1)+βε_(n)+{tilde over(θ)}′_(n),   Eq. (3b)

{tilde over (θ)}_(n)={tilde over (θ)}_(n-1)+αε_(n)+{tilde over(θ)}′_(n),   Eq. (3c)

where 0≦α≦1, 0≦β≦1 and 0≦γ≦1. In the same manner, this tracking can befurther generalized to an n-th order PLL. Note that this 3-rd order PLLcan track not only static frequency errors but also time-varyingfrequency errors.

Note that the above n-th order phase reference tracking algorithm may beapplied to any phase-modulated signals. In general, the inputs of thephase reference tracking unit 120 are the received phase r_(n) 111 andthe re-modulation phase signal ŝ_(n-d) 131. The output of the phasereference tracking unit 120 is the estimated transmit phase {tilde over(s)}_(n) 141, after proper phase/frequency error correction, at thereceiver. If required, the overall block diagram may be re-organized tosave computational power and/or hardware size.

For clearer explanations, consider an M-ary PSK signal. In thetransmitter (TX), k (=log₂ M) information bits are mapped to one of theM phases. Let a_(n) and s_(n) be the n-th symbol with k information bitsand its corresponding mapped phase, respectively. This, the transmitphase, s_(n) may be represented as

s_(n)=

(a_(n)), n=0, 1, . . . , M−1,   Eq. (4)

where

(•) denotes the phase-mapping function. Note the phase mapping for M=2is shown in TABLE 2. In the proposed MPSK receiver (RX) shown in FIG. 2,the phase of a received phase r_(n) 111 may be represented as

r _(n) =s _(n)+θ_(n),   Eq. (5)

where θ_(n) is the phase mismatching caused by the phase mismatchingbetween the TX and the RX. The proposed second order PLL for decodings_(n) and tracking θ_(n) for a received MPSK signal is as follows:

Decoding/Phase-Tracking algorithm for MPSK signals (FIG. 2)

For n=0 to N-1

{tilde over (s)} _(n) =r _(n)−{tilde over (θ)}_(n-1)   Eq. (6a)

â _(n)=

⁻¹({tilde over (s)} _(n))   Eq. (6b)

ŝ _(n)=

(â _(n))   Eq. (6c)

ε_(n) ={tilde over (s)} _(n) −ŝ _(n)   Eq. (6d)

{tilde over (θ)}′_(n)={circumflex over (θ)}′_(n-1)+βε_(n)   Eq. (6e)

{tilde over (θ)}_(n)={tilde over (θ)}_(n-1)+αε_(n)+{tilde over (θ)}′_(n)  Eq. (6f)

An PSK coherent decoder 210 comprises a de-mapping unit and a mappingunit. The function

(•) is the de-mapping unit 213, i.e., the inverse function of

(•). This de-mapping unit is for decoding an MPSK signal to produce adecoded symbol â_(n) 212. This decoded symbol â_(n) 212 is mapped againto generate a re-modulation phase signal ŝ_(n) 149 with the mapping unit211. Note an example de-mapping table is given in TABLE 1 and thecorresponding mapping table is given in TABLE 2 for a BPSK modulatedsignal.

Inside the phase reference tracking unit 220, the n-th estimatedtransmit phase {tilde over (s)}_(n) 141, is calculated by subtractingthe previous phase reference estimate {tilde over (θ)}_(n-1) 142 fromr_(n) 111. Initial phase reference {tilde over (θ)}⁻¹ is assumed to beestimated with the help of a training sequence which is known to both TXand RX. Even if this initial phase reference {tilde over (θ)}⁻¹ iswell-estimated, this reference may be further tracked for better Rxperformance. Moreover, this invention may help to track phase referencewith the phase variations during receiving due to imperfection in the Txor the Rx path.

Then, an error ε_(n) 145 is calculated by subtracting ŝ_(n) 149 from{tilde over (s)}_(n) 141. Note that ε_(n) 145 tends to be smaller with amore accurate {tilde over (θ)}_(n-1) 142. A phase correction factor dueto FO between the TX and the RX, {tilde over (θ)}′_(n) 147, is obtainedwith ε_(n) 145 and β 146 from the previous estimate {tilde over(θ)}′_(n-1). Note: Units 125 and 129 represent “sample delays” and thecircuitry shown in 220 implements Eq. (6e). The initial estimate {tildeover (θ)}′₁ may be set to zero or previous estimate based on a trainingsequence. Finally, a phase reference estimate {tilde over (θ)}_(n) 148is updated with ε_(n) 145, α 143 and {tilde over (θ)}′_(n) 147 from{tilde over (θ)}_(n-1) 142 using Eq. (6f). This process shall berepeated until every symbol is decoded.

This invention can be also applied to DPSK signals. DPSK signals arepopular for many communication systems due to the simple non-coherentdetections even though coherent detections outperform non-coherentdetections by up to 3 dB. Those non-coherent detection losses may bereduced by reliable phase reference tracking.

U.S. Pat. No. 7,245,672 disclosed the so-called ‘semi-coherentdemodulation for DPSK signals' (FIG. 3) which is similar to the phasetracking algorithm for PSK signals with a first-order PLL, but hisalgorithm does not track the higher-order phase variations. Moreover,the phase error measurement is based on the transmit phaseconstellations. That means, the phase error measurement may be not asreliable as that of the present invention (shown later) since the numberof constellations may be larger than M for M-ary DPSK. For example,Bluetooth adopts π/4 DQPSK of which number of constellations is notfour, but eight. Another disadvantage of the algorithm is that singleerror in PSK decoder (unit 310) causes double errors after differentialdecoding (shown later).

Smit's decoding algorithm for DPSK signals (FIG. 3)For n=0 to N-1

{tilde over (s)} _(n) =r _(n)−{tilde over (θ)}_(n-1)   Eq. (7a)

ŝ _(n) =

D({tilde over (s)} _(n))   Eq. (7b)

ε_(n) ={tilde over (s)} _(n) −ŝ _(n)   Eq. (7c)

{tilde over (θ)}_(n)={tilde over (θ)}_(n-1)+αε_(n)   Eq. (7d)

â _(n)=

(ŝ _(n) −ŝ _(n-1))   Eq. (7e)

where

D(a) is a function that gives out the phase of the closest constellationto a. For π/4 DQPSK, the number of the possible ŝ_(n) 149 values iseight, not four due to the π/4 shifting. In this case, a less reliablephase error estimate, ε_(n) 145, is generated per Eq. (7c). A PSKdecoder unit 310 decodes a PSK signal with the first-order PLL inphase-domain, generating the re-modulation phase signal ŝ_(n) 149. Then,a differential decoder unit 320 differentially the re-modulation phasesignal ŝ_(n) 149, generating â_(n) 212. Due to the differential decodingin Eq. (7e), single error in ŝ_(n) 149 causes double errors in â_(n) 212for a DPSK signal.

Here, we propose a method for a DPSK signal to overcome thedisadvantages of the prior invention such as the first-order PLLtracking limitation, unreliable phase error estimate for π/4 DQPSK, andthe double errors. Let's consider an M-ary DPSK signal similar to a MPSKsignal. In the TX, k (=log₂ M)information bits are mapped to one of theM phases. Let a_(n) and x_(n) be the n-th symbol with k information bitsand its corresponding mapped phase, respectively. This phase, x_(n) maybe represented as

x _(n)=

(a _(n)), n=0, 1, . . . , N−1.   Eq. (8)

Those mapped phases are accumulated before transmitting. In the RX, thephase of the received phase r_(n) 111 may be represented as

$\begin{matrix}{{r_{n} = {s_{n} + \theta_{n}}},{{{where}\mspace{14mu} s_{n}} = {\sum\limits_{m = 0}^{n}x_{n}}}} & {{Eq}.\mspace{14mu} (9)}\end{matrix}$

where θ_(n) is the phase mismatching between the TX and the RX asprevious explained. The proposed algorithm of θ_(n) estimation for DPSKis as follows:

A Phase Tracking and Decoding algorithm for DPSK Signals (FIG. 4)

For n=1 to N-1

{tilde over (s)}_(n) =r _(n)−{tilde over (θ)}_(n-1)   Eq. (10a)

{tilde over (x)} _(n) ={tilde over (s)} _(n) −ŝ _(n-1)   Eq. (10b)

â _(n) =M ⁻¹({tilde over (x)} _(n))   Eq. (10c)

{circumflex over (x)} _(n)=

(â _(n))   Eq. (10d)

ŝ _(n) =ŝ _(n-1) +{circumflex over (x)} _(n)   (10e)

ε_(n) ={tilde over (s)} _(n) −ŝ _(n)   Eq. (10f)

{tilde over (θ)}′_(n)={tilde over (θ)}′_(n-1)+βε_(n)   Eq. (10g)

{tilde over (θ)}_(n)={tilde over (θ)}_(n-1)+αε_(n)+{tilde over (θ)}′_(n)  Eq. (10h)

This algorithm is similar to that for MPSK signals except the coherentdecoder 410. Because the mapped phase x_(n) is accumulated in the TX,ŝ_(n-1) is subtracted from {tilde over (s)}_(n) 141 before de-mapping,as is shown in Eq. (10b) and illustrated in coherent decoder 410. Theinitial phase reference {tilde over (θ)}₀ may be set to r₀ or a previousestimate. The other initial estimate {tilde over (θ)}′₀ may be set tozero or a previous estimate.

This algorithm can be re-written without {tilde over (s)}_(n) 141 andŝ_(n) 149 as follows:

An Alternative implementation of phase-tracking and decoding algorithmfor DPSK Signals

For n=1 to N-1

$\begin{matrix}{{\overset{\sim}{x}}_{n} = {r_{n} - {\sum\limits_{m = 1}^{n - 1}{\hat{x}}_{m}} - {\overset{\sim}{\theta}}_{n - 1}}} & {{Eq}.\mspace{14mu} \left( {11a} \right)} \\{{\hat{a}}_{n} = {\mathcal{M}^{- 1}\left( {\overset{\sim}{x}}_{n} \right)}} & {{Eq}.\mspace{14mu} \left( {11b} \right)} \\{{\hat{x}}_{n} = {\mathcal{M}\left( {\hat{a}}_{n} \right)}} & {{Eq}.\mspace{14mu} \left( {11c} \right)} \\{ɛ_{n} = {{\overset{\sim}{x}}_{n} - {\hat{x}}_{n}}} & {{Eq}.\mspace{14mu} \left( {11d} \right)} \\{{\overset{\sim}{\theta}}_{n}^{\prime} = {{\overset{\sim}{\theta}}_{n - 1}^{\prime} + {\beta ɛ}_{n}}} & {{Eq}.\mspace{14mu} \left( {11e} \right)} \\{{\overset{\sim}{\theta}}_{n} = {{\overset{\sim}{\theta}}_{n - 1} + {\alpha \; ɛ_{n}} + {\overset{\sim}{\theta}}_{n}^{\prime}}} & {{Eq}.\mspace{14mu} \left( {11f} \right)}\end{matrix}$

The algorithm for DPSK signals is further simplified by introducing{tilde over (φ)}_(n). Let

$\begin{matrix}{{\overset{\sim}{\varphi}}_{n} = {{\sum\limits_{m = 0}^{n}{\hat{x}}_{m}} + {{\overset{\sim}{\theta}}_{n}.}}} & {{Eq}.\mspace{11mu} (12)}\end{matrix}$

Then,

{tilde over (x)} _(n) =r _(n)−{tilde over (φ)}_(n-1),   Eq. (13)

Since {tilde over (θ)}_(n)={tilde over (θ)}_(n-1)+αε_(n)+{tilde over(f)}_(n), φ_(n) can be derived as follows:

$\begin{matrix}\begin{matrix}{{\overset{\sim}{\varphi}}_{n} = {{\sum\limits_{m = 0}^{n}{\hat{x}}_{m}} + {\overset{\sim}{\theta}}_{n - 1} + {\alpha \cdot ɛ_{n}} + {\overset{\sim}{f}}_{n}}} \\{= {{\hat{x}}_{n} + {\sum\limits_{m = 0}^{n - 1}{\hat{x}}_{m}} + {\overset{\sim}{\theta}}_{n - 1} + {\alpha \cdot ɛ_{n}} + {\overset{\sim}{f}}_{n}}} \\{= {{\hat{x}}_{n} + {\overset{\sim}{\varphi}}_{n - 1} + {\alpha \cdot ɛ_{n}} + {\overset{\sim}{f}}_{n}}} \\{= {{\overset{\sim}{x}}_{n} - ɛ_{n} + {\overset{\sim}{\varphi}}_{n - 1} + {\alpha \cdot ɛ_{n}} + {\overset{\sim}{f}}_{n}}} \\{= {r_{n} - {\left( {1 - \alpha} \right) \cdot ɛ_{n}} + {\overset{\sim}{f}}_{n}}}\end{matrix} & {{Eq}.\mspace{14mu} (14)}\end{matrix}$

Therefore, the algorithm for DPSK signals may be written as follows:

An Alternative Algorithm for Phase-Tracking and Decoding of DPSK Signals(FIG. 5)

For n=1 to N-1

{tilde over (x)} _(n) =r _(n)−{tilde over (φ)}_(n-1)   Eq. (15a)

â _(n)=

({tilde over (x)} _(n))   Eq. (15b)

{circumflex over (x)} _(n)=

(â _(n))   Eq. (15c)

ε_(n) ={circumflex over (x)} _(n) −{circumflex over (x)} _(n)   Eq.(15d)

{tilde over (θ)}′_(n)={tilde over (θ)}′_(n-1)+βε_(n)   Eq. (15e)

{tilde over (φ)}_(n) =r _(n)−(1−α)·ε_(n)+{tilde over (θ)}′_(n)   Eq.(15f)

FIG. 5 shows the corresponding implementation, compared to the previousalgorithm, accumulation of {circumflex over (x)}_(n) 414 is no longerrequired in this algorithm. In addition, this algorithm becomes thecommonly used non-coherent detection when setting α=1 and β={tilde over(θ)}′₀=0. As shown in this alternative algorithm for DPSK signals, thephase reference tracking unit 120 and coherent decoder 130 may becombined to save computation power and/or hardware size by sharing unitsand/or re-organizing units.

This DPSK phase-tracking and decoding algorithm is simpler than theSmit's algorithm if a higher-order PLL for phase-tracking is disabled.Moreover, this is more robust for π/4 DPSK signals than the Smit'sbecause the hard-decisional error probability is smaller with a greaterdistance among a four-phase constellation set than an eight-phaseconstellation set. In Smit's algorithm, ŝ_(n) 149 is set to the closestconstellation from {tilde over (s)}_(n) 141 (Eq. (7b)). Since the numberof constellations is eight, the minimum phase distance amongconstellations is only π/4. For the current invention, the minimum phasedistance to decide {circumflex over (x)}_(n) 414 is π/2. Note that thisalgorithm is also good for heavy phase variations caused by frequencyerrors thanks to the higher order tracking. The double errors are alsoavoidable with this invention. Current error in â_(n) 212 may causephase tracking degraded but not necessarily cause the next symbol error.In Smit's, an error in ŝ_(n) 149 causes double errors for sure with aDPSK signal which is not shifted. Note that single error is stillpossible with Smit's for a π/4 shifted DQPSK signal.

Even though the proposed algorithm shown in the above are all 1st or 2ndorder PLL's, one can easily generalize it to a 3rd order PLL as follows:

For n=1 to N-1

{tilde over (x)} _(n) =r _(n)−{tilde over (φ)}_(n-1)   Eq. (16a)

â _(n)=

({tilde over (x)} _(n))   Eq. (16b)

{circumflex over (x)} _(n)=

(â _(n))   Eq. (16c)

ε_(n) ={tilde over (x)} _(n) −{circumflex over (x)} _(n)   Eq. (16d)

{tilde over (θ)}″_(n)={tilde over (θ)}″_(n-1)+γε_(n) (where 0≦γ≦1)   Eq.(16e)

{tilde over (θ)}′_(n)={tilde over (θ)}′_(n-1)+βε_(n)+{tilde over(θ)}′_(n)   Eq. (16f)

{tilde over (φ)}_(n) =r _(n)−(1−α)·ε_(n)+{tilde over (θ)}′_(n)   Eq.(16g)

When compared to a 2nd order PLL as shown in Eq. (15), the onlydifference in the above is the addition of {tilde over (θ)}″_(n), whichcan be used to track the FO variations. For Bluetooth applications, onefound the 3rd order PLL, proposed in the above, offers the bestperformance against dirty packets, for which a FO and a sine-wave basedfrequency variation are both added to the transmitted BT EDR packets.

1. A method used for phase reference tracking of digital phase modulatedsignals in the receiver, comprising the steps of: converting a receivedcomplex signal to the received phase r_(n); feeding the received phaser_(n) to a phase reference tracking unit; producing an estimatedtransmit phase {tilde over (e)}_(n) from the phase reference trackingunit; feeding the estimated transmit phase {tilde over (s)}_(n) to acoherent decoder; and producing a decoded symbol â_(n) from the coherentdecoder.
 2. A method used for phase reference tracking of digital phasemodulated signals in the receiver as claimed in claim 1, wherein thereceived complex signal can be encoded by BPSK, MPSK, PSK and DPSKmodulation systems.
 3. A method used for phase reference tracking ofdigital phase modulated signals in the receiver as claimed in claim 1,wherein the received phase r_(n) can be converted to different formsaccording to the received complex signal.
 4. A method used for phasereference tracking of digital phase modulated signals in the receiver asclaimed in claim 1, wherein the procedure of producing an estimatedtransmit phase {tilde over (s)}_(n) further comprising the steps of:subtracting a previous phase reference estimate {tilde over (θ)}_(n-1)from a received phase r_(n); producing a tracking error ε_(n) bysubtracting a re-modulation phase signal ŝ_(n) from an estimatedtransmit phase {tilde over (s)}_(n); scaling the tracking error ε_(n) bya value of β; adding the scaled of tracking error βε_(n) with a previousphase correction factor {tilde over (θ)}′_(n-1) and derive a phasecorrection factor {tilde over (θ)}′_(n); scaling the tracking errorε_(n) by a value of α; adding the scaled of tracking error αε_(n) withthe phase correction factor {tilde over (θ)}′_(n); and adding the scaledof tracking error αε_(n) with the phase correction factor {tilde over(θ)}′_(n) with the previous phase reference estimate {tilde over(θ)}_(n-1) and derive the phase reference estimate {tilde over (θ)}_(n).5. A method used for phase reference tracking of digital phase modulatedsignals in the receiver as claimed in claim 1, wherein the procedure ofproducing an estimated transmit phase {tilde over (s)}_(n) furthercomprising the steps of: subtracting a previous phase reference estimate{tilde over (θ)}_(n-1) from a received phase r_(n); adding a delay (d)to an estimated transmit phase {tilde over (s)}_(n); producing atracking error ε_(n) by subtracting a re-modulation phase with a delay(d) ŝ_(n-d) from a re-modulation phase with a delay (d)ŝ_(n-d); scalingthe tracking error ε_(n) by a value of β; adding the scaled of trackingerror βε_(n) with a previous phase correction factor {tilde over(θ)}′_(n-1) and derive a phase correction factor {tilde over (θ)}′_(n);scaling the tracking error ε_(n) by a value of α; adding the scaled oftracking error αε_(n) with the phase correction factor {tilde over(θ)}′_(n); and adding the scaled of tracking error αε_(n) with the phasecorrection factor {tilde over (θ)}′_(n) with the previous phasereference estimate {tilde over (θ)}_(n-1) and derive the phase referenceestimate {tilde over (θ)}_(n). wherein the delay (d) is used forgenerating the estimated transmit phase {tilde over (s)}_(n) withcorrect timing.
 6. A method used for phase reference tracking of digitalphase modulated signals in the receiver as claimed in claim 1, whereinthe procedure of producing a decoded symbol â_(n) further comprising thesteps of: feeding an estimated transmit phase {tilde over (s)}_(n) to acoherent decoder; de-mapping the estimated transmit phase {tilde over(s)}_(n); producing a decoded symbol â_(n); mapping the decoded symbolâ_(n); and producing a re-modulation phase signal ŝ_(n); wherein there-modulation phase signal ŝ_(n) is feed to a phase reference trackingunit and used for the calculation of a tracking error ε_(n).
 7. A methodused for phase reference tracking of digital phase modulated signals inthe receiver as claimed in claim 1, wherein the method is generalizedwith n-th order tracking.
 8. An apparatus used for phase referencetracking of digital phase modulated signals in the receiver, comprising:a complex-to-phase converter, used for converting the in-phase (I_(n))and the quadrature (Q_(n)) components of a received complex signal to areceived phase r_(n); a phase reference tracking unit, electricallyconnected to the complex-to-phase converter, used for producing anestimated transmit phase {tilde over (s)}_(n); and a coherent decoder,electrically connected to the phase reference tracking unit, used forproducing a decoded symbol â_(n) and sending a re-modulation phasesignal ŝ_(n) to the phase reference tracking unit.
 9. An apparatus usedfor phase reference tracking of digital phase modulated signals in thereceiver as claimed in claim 8, wherein the apparatus used for phasereference tracking of digital phase modulated signals in the receivercan be applied in BPSK, MPSK, PSK and DPSK modulation systems.
 10. Anapparatus used for phase reference tracking of digital phase modulatedsignals in the receiver as claimed in claim 8, wherein the receivedcomplex signal can be encoded by BPSK, MPSK, PSK and DPSK modulationsystems.
 11. An apparatus used for phase reference tracking of digitalphase modulated signals in the receiver as claimed in claim 8, whereinthe received phase r_(n) can be converted to different forms accordingthe received complex signal.
 12. An apparatus used for phase referencetracking of digital phase modulated signals in the receiver as claimedin claim 8, wherein the types of the coherent decoder can be selectedaccording to BPSK, MPSK and DPSK modulation systems.
 13. An apparatusused for phase reference tracking of digital phase modulated signals inthe receiver as claimed in claim 8, wherein the phase reference trackingunit further comprising: a first subtracter, used for subtracting theprevious phase reference estimate {tilde over (θ)}_(n-1) from thereceived phase r_(n) and producing the estimated transmit phase {tildeover (s)}_(n); a second subtracter, electrically connected to thecoherent decoder, used for subtracting the a re-modulation phase signalŝ_(n) from the estimated transmit phase {tilde over (s)}_(n) andproducing a tracking error ε_(n); a first multiplier, electricallyconnected to the second subtracter, used for scaling the tracking errorε_(n) by a value of β; a first adder, electrically connected to thefirst multiplier, used for adding a scaled tracking error βε_(n) and aprevious phase correction factor {tilde over (θ)}′_(n-1); a first sampledelay unit, electrically connected to the first adder, used for thetaking the phase correction factor {tilde over (θ)}′_(n) to the previousstate of {tilde over (θ)}′_(n-1) and providing a feedback signal ofprevious phase correction factor {tilde over (θ)}′_(n-1) to the firstadder. a second multiplier, electrically connected to the secondsubtracter, used for scaling the tracking error ε_(n) by a value of α; asecond adder, electrically connected to the second multiplier, used foradding a scaled tracking error αε_(n) and the phase correction factor{tilde over (θ)}′_(n); a third adder, electrically connected to thesecond adder, used for adding the previous phase reference estimate{tilde over (θ)}_(n-1), the scaled tracking error αε_(n) and the phasecorrection factor {tilde over (θ)}′_(n); and a second sample delay unit,electrically connected to the second adder, used for the taking thephase reference estimate {tilde over (θ)}_(n) to the previous state{tilde over (θ)}_(n-1) and providing a feedback signal of previousreference estimate {tilde over (θ)}_(n-1) to the third adder and thefirst subtracter.
 14. An apparatus used for phase reference tracking ofdigital phase modulated signals as claimed in claim 13, wherein thephase reference tracking unit tracks phase with a second-orderphase-locked-loop.
 15. An apparatus used for phase reference tracking ofdigital phase modulated signals as claimed in claim 13, wherein thephase tracking unit is generalized with n-th order tracking by addingthe order of phase-locked-loop.
 16. An apparatus used for phasereference tracking of digital phase modulated signals as claimed inclaim 13, wherein the construction of the block diagram of the apparatusmay be modified and/or simplified with combining the phase referencetracking units and the coherent decoder units by removing redundantunits and/or re-organizing the block diagrams.
 17. An apparatus used forphase reference tracking of digital phase modulated signals in thereceiver as claimed in claim 8, wherein the phase reference trackingunit further comprising: a first subtracter, used for subtracting theprevious phase reference estimate {tilde over (θ)}_(n-1) from thereceived phase r_(n) and producing the estimated transmit phase {tildeover (s)}_(n); a coherent decoder, electrically connected to the firstsubtracter, used for compensating the delay (d) caused in the coherentdecoder and generating the estimated transmit phase {tilde over (s)}_(n)with correct timing; a second subtracter, electrically connected to thecoherent decoder, used for subtracting the a re-modulation phase signalwith a delay (d) ŝ_(n-d) from the estimated transmit phase with a delay(d) {tilde over (s)}_(n-d) and producing a tracking error ε_(n); a firstadder, electrically connected to the first multiplier, used for adding ascaled tracking error βε_(n) and a previous phase correction factor{tilde over (θ)}′_(n-1); a first sample delay unit, electricallyconnected to the first adder, used for the taking the phase correctionfactor {tilde over (θ)}′_(n) to the previous state of {tilde over(θ)}′_(n-1) and providing a feedback signal of previous phase correctionfactor {tilde over (θ)}′_(n-1) to the first adder. a second multiplier,electrically connected to the second subtracter, used for scaling thetracking error ε_(n) by a value of α; a second adder, electricallyconnected to the second multiplier, used for adding a scaled trackingerror αε_(n) and the phase correction factor {tilde over (θ)}′_(n); athird adder, electrically connected to the second adder, used for addingthe previous phase reference estimate {tilde over (θ)}_(n-1), the scaledtracking error αε_(n) and the phase correction factor {tilde over(θ)}′_(n); and a second sample delay unit, electrically connected to thesecond adder, used for the taking the phase reference estimate {tildeover (θ)}_(n) to the previous state {tilde over (θ)}_(n-1) and providinga feedback signal of previous reference estimate {tilde over (θ)}_(n-1)to the third adder and the first subtracter. wherein the delay (d) ofestimated transmit phase {tilde over (s)}_(n) is caused by the coherentdecoder and results an estimated transmit phase with a delay (d) {tildeover (s)}_(n-d).
 18. An apparatus used for phase reference tracking ofdigital phase modulated signals as claimed in claim 16, wherein thephase reference tracking unit tracks phase with a second-orderPhase-locked-loop.
 19. An apparatus in phase reference tracking asclaimed in claim 17, wherein the phase tracking unit is generalized withn-th order tracking.
 20. An apparatus used for phase reference trackingof digital phase modulated signals as claimed in claim 17, wherein theconstruction of the block diagram of the apparatus may be modifiedand/or simplified with combining the phase reference tracking units andthe coherent decoder units by removing redundant units and/orre-organizing the block diagrams.